don't use wrapping paper. Thats a hazard. It's not rated for heat like mylar and poly material is. It will melt and/or start a fire. Even mylar can burn if it's too close to an HID bulb.
Not to mention you're wasting light, because it's really not a reflective surface at all. It's like a holographic type reflection, it will actually absorb the light.
Use a flat white paint, repaint the closet and you're good to go. I would go out and build a barrier and shorten the closet width if you need to, after you find out how many plants you want t ogrow, and take new measurements and this will help reduce the amount of lumens you need.
Don't forget a good reflector as well, and remember a 400W HPS only covers approx. 55000 lumens (with a fresh bulb). So, you'd need at least a 600w+ to get some kind of good coverage, and you would want to get an MH Conversion bulb to veg with.